Harmonic Series

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Harmonic Series

Post by synkrotron » Tue May 19, 2020 5:06 am

Hi Peeps :)

I want to talk about the Harmonic Series with regards to sound design.

So I did an advance search for Harmonic Series just within the Synthesis Techniques forum.

I was surprised that nothing came up at all about this topic.

Am I in the right place? Am I missing something? Should I look elsewhere?

Or should I kick my own discussion in this new topic?


cheers

andy

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Re: Harmonic Series

Post by wuff_miggler » Tue May 19, 2020 6:39 am

i think being that the basis of additive synthesis is adding sine waves together - its kind of implied?

definition of additive synthesis from wiki:

Additive synthesis is a sound synthesis technique that creates timbre by adding sine waves together. The timbre of musical instruments can be considered in the light of Fourier theory to consist of multiple harmonic or inharmonic partials or overtones.

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Re: Harmonic Series

Post by synkrotron » Tue May 19, 2020 10:34 am

Hi :)
wuff_miggler wrote:
Tue May 19, 2020 6:39 am
i think being that the basis of additive synthesis is adding sine waves together - its kind of implied?
Yes, I suppose it is.

I just thought I'd have a look around the so called "Synthesis Techniques" forum to see what I could find on the subject.

Like I said, an advance search reveals nothing.

I have just done another advance search on the term "additive" and only three posts are shown, one of them this post.

The other two are the one you posted about Audio Analysis and another about FM patches sounding like bells.

No discussion about additive synthesis and the harmonic series.

I can only assume that the subject matter is boring or else this sub-forum is relatively new. I've been a member at MW for three years but I've never posted in this particular sub-forum before.


Anyway, I am here to admit that despite now nearly 60, I have never really bothered with additive synthesis. I am very much a subtractive synthesis person, for some reason. I suppose it must be down to my laziness and being so comfortable with that little corner of "sound design."

I have been watching videos of two modules over the last couple of days, the Xaoc Odessa and the new Ensemble Oscillator from 4ms, both based on additive synthesis and both quite desirable modules, if not a touch out of my budget at the moment. It is because of this that I have decided to look further into the world of additive synthesis as I quite like the sounds that come from that.

And this is where I come to the Harmonic Series because it is the science and maths associated with that that gives us some of those pleasant sounds.

Because I am not likely to be able to splash out £400 or so on a new module like that I thought I would look at what I have in my system.

I tried a simple patch earlier this morning consisting, initially, of four Distings each outputting a sine wave. One was tuned to the 1st harmonic, or fundamental, the second to the 2nd harmonic, and so on. By running each oscillator into one of my Doepfer mixers, and with the aid of the SPAN spectrum analyser in REAPER, I was able to develop a saw wave. Okay, only the fundamental and three "harmonic overtones," but I thought it sounded quite interesting.

I then run each oscillator into a VCA before running into the mixer. Each VCA was modulated by LFO's with slightly different rates. The resulting drone was very pleasant to my ears.

I then set up a simple sequence with the Metropolis. I ran the output of the mixer to a low pass gate with the gate from the Metropolis driving that. The pitch CV from the Metropolis was sent to a buffered multi so that I could send on that pitch CV to each oscillator.

Again, I was quite pleased with the end result.

I'm sure this sounds so simple to many but to me it has been quite an epiphany.

For what it is worth I will share a couple of videos that I ran into this morning:-





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Re: Harmonic Series

Post by a100user » Tue May 19, 2020 11:25 am

It’s these moments the reinvigorate me with my kit. Congratulations on taking the plunge to discover new sounds with what you have rather just buying another module.
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Re: Harmonic Series

Post by EATyourGUITAR » Tue May 19, 2020 11:42 am

maybe the reason search returned nothing is because harmonic series is a term reserved for mathematics. it predates any usage by fourier, shannon et all. the fourier series in math is indeed a kind of harmonic series. however, the harmonic series is not really a term as much as a harmonic series is a descriptive term.

https://en.wikipedia.org/wiki/Harmonic_ ... thematics)

https://en.wikipedia.org/wiki/Harmonic_series_(music)

https://en.wikipedia.org/wiki/Fourier_series

I find it hilarious that the sources in wikipedia's harmonic series (music) has no evidence that it exists. the article from 1994 does not exist. the book from 1987 makes no mention of the harmonic series in the book! Andrew is wearing too much make up going hollywood. He already damaged his ears and made a pile of money I don't know why he keeps going. his audience is noobs so I guess it doesn't matter that he uses incorrect information from wikipedia. no one will ever know.
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Re: Harmonic Series

Post by galanter2 » Tue May 19, 2020 12:53 pm

One lesson from additive synthesis is that you can have several different looking results that sound the same. To approximate a sawtooth, for example, you have to get the right sine wave relationships both in frequency AND phase.

Additive synthesis has a deeper history in the realm of academic computer music. It's hard to create easy to use additive synthesis tools for pop musicians.

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Re: Harmonic Series

Post by synkrotron » Tue May 19, 2020 1:09 pm

a100user wrote:
Tue May 19, 2020 11:25 am
Congratulations on taking the plunge to discover new sounds with what you have rather just buying another module.
Thank you :mrgreen:

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Re: Harmonic Series

Post by synkrotron » Tue May 19, 2020 1:10 pm

EATyourGUITAR wrote:
Tue May 19, 2020 11:42 am
his audience is noobs
Yeah, that's me :oops:

Oh, thanks for the links... More stuff to blow my mind...

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Re: Harmonic Series

Post by synkrotron » Tue May 19, 2020 1:19 pm

galanter2 wrote:
Tue May 19, 2020 12:53 pm
To approximate a sawtooth, for example, you have to get the right sine wave relationships both in frequency AND phase.
Well, I have a lot to learn, obviously. And at the end of the day I may not even be doing true additive synthesis. I mean, does adding different sine oscillators via a simple mixer actually class as additive synthesis.

Whether it does or doesn't I'm not totally bothered. So long as I get interesting sounds.

I don't intend sticking with the humble sine wave either. I'll also be experimenting with dropping at least one other waveform in there, and even adding some low pass filtering into the mix.

I think that exploring additive synthesis is a really interesting thing for me to do but I am prone to go off at a tangent...

cheers

andy

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Re: Harmonic Series

Post by wuff_miggler » Tue May 19, 2020 3:56 pm

@synkroton - i hope my comment wasnt seen as douchery, was just hopefully trying to answer the question as to "why".
also - just keep in mind - Additive synthesis is kinda like FM synthesis - hard to get your head around.

You might want to look into some Manuals and in particular "the Wizoo Book" for the Kawai K500 which had a very unique synthesis engine - 128 harmonics, with 128 formant filters on each - all automatable.

perhaps you might get some more info out of it - about this technique. The wizoo book from memory goes through techniques on how to recreate certain acousic and synth sounds - it would help if you had the synth in front of you to actually make the sounds though...hmmm :D

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Re: Harmonic Series

Post by synkrotron » Tue May 19, 2020 5:16 pm

wuff_miggler wrote:
Tue May 19, 2020 3:56 pm
i hope my comment wasnt seen as douchery
No, not at all :)
hard to get your head around.
I agree, but I'm getting there :tu:
You might want to look into some Manuals and in particular "the Wizoo Book" for the Kawai K500 which had a very unique synthesis engine - 128 harmonics, with 128 formant filters on each - all automatable.

perhaps you might get some more info out of it - about this technique. The wizoo book from memory goes through techniques on how to recreate certain acousic and synth sounds - it would help if you had the synth in front of you to actually make the sounds though...hmmm :D
Well, like you say, would help if I had that synth, which I don't.

I'm not that interested in achieving any particular sound, acoustic or what ever. I am happy that I'm exploring something that I should have done a long time ago. Either in software or hardware. I've been "sound designing" for quite a while :mrgreen:


Thanks again for your input, it is all appreciated :)

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Re: Harmonic Series

Post by Umcorps » Wed May 20, 2020 2:10 am

One thing that really does help wit this is having a spectrometer so you can actually see what you are doing as well as hear it. I use FFT Plot on iOS (https://apps.apple.com/us/app/fft-plot/id569468015) but there are many other alternatives

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Re: Harmonic Series

Post by synkrotron » Wed May 20, 2020 4:10 am

Hi :)
Umcorps wrote:
Wed May 20, 2020 2:10 am
One thing that really does help wit this is having a spectrometer so you can actually see what you are doing as well as hear it. I use FFT Plot on iOS (https://apps.apple.com/us/app/fft-plot/id569468015) but there are many other alternatives
Yeah, I agree, and I'm using Voxengo SPAN for now because I always send my audio through REAPER anyway. I have other options, but SPAN appears to be doing the business. I have it set so that it displays a more narrow band of frequencies but I may have to play with that setting so that is shows an even tighter band.

I also have Melda's free oscilloscope although I have hardly ever used it. I'll dust it off to see what it tells me.


cheers

andy

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Re: Harmonic Series

Post by Keltie » Wed May 20, 2020 5:17 am

TBH, I find the basic concept of additive pretty easy to get my head around. I think the reason it’s implemented less in musical instruments is that ergonomically it’s a pain, and requires a lot of hardware, in analogue.

Would you rather select a sawtooth in a straight up analogue osc, and filter it using an envelope, or line up n sine waves, keeping the correct volume ratios, and then automate n vcas to alter those ratios over time? In theory at least, the results would be much the same.

I tried out programming additively just for kicks using a Casio fz1 back in the 90s, with 64 sines. Interesting, but massively labour intensive.

Andy, some thoughts for your experiments. The formula for a saw wave: if the fundamental sine frequency F is volume level 1.0, then frequency 2F is 0.5, 3F 0.33 etc. If you scope that, the more sines you have, the more closely you approximate a sawtooth.

For square, omit any even F frequency multiplier.

For triangle, omit any even F frequency multiplier, and also divide the fundamental volume V by the frequency ratio squared. So F1= V F3= V/9, F5= V/25.

All harmonics should be in phase with the fundamental.

Mordax data, or almost any DAW based EQ will show you what harmonics are doing very easily, just run a sawtooth in tuned at 50Hz... you can see the harmonics easily.

Digital is absolutely the way to go for additive. Odessa looks very interesting. Wavetables can get you part way there, for example, E352/370 have some tables where harmonics fade up through the table.

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Re: Harmonic Series

Post by cornutt » Wed May 20, 2020 9:27 pm

I've done some additive synthesis. IMO it's a synthesis method that is better done in software. You'd need a rather large system full of VCOs, LFOs, EG, VCAs and mixers to duplicate what you can do with a fairly basic additive plug-in like Minky Starshine (one of my most-used plug-ins). It is, however, practical to do a sort of hybrid method in software. E.g:

1. Mix a few sine waves, set to lower harmonics, and run them through a VCA with an envelope, and then mix that with the output of a conventional subtractive patch.

2. Do a simple mix of a few sine waves and then use them as the carrier in a ring modulator patch.

3. MIx several sine waves as, say, a fundamental with a 3rd, 6th, and 8th harmonic. (You'll probably have to use a frequency counter to do this accurately.) Then... pull out the patch cord for the fundamental, and mix the rest and give them a percussive envelope. You'll get bell-like sounds.

You can also try doing additive techniques with triangle waves. They have a little bit of harmonic content, and will add more "body" to additive patches with only a few oscillators, but not so much that the patch starts to dissolve into chaos the way it would if you were using, say, sawtooth waves.
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Re: Harmonic Series

Post by synkrotron » Thu May 21, 2020 4:29 am

Hi Keltie :)
Keltie wrote:
Wed May 20, 2020 5:17 am
TBH, I find the basic concept of additive pretty easy to get my head around. I think the reason it’s implemented less in musical instruments is that ergonomically it’s a pain, and requires a lot of hardware, in analogue.
Yes, it certainly seems that way, now that I have researched this some more.
Would you rather select a sawtooth in a straight up analogue osc, and filter it using an envelope, or line up n sine waves, keeping the correct volume ratios, and then automate n vcas to alter those ratios over time? In theory at least, the results would be much the same.
For many years, reaching for that sawtooth, or what ever, has always been the case and is why where I am now, an additive noob.

I am quickly coming to the conclusion that, with what I have to hand in my system, I am unlikely to go all out additive. But it is amazing what you can do with just four or five sine waves and some VCA's/LFO's. That has definitely opened up the horizon for me. Not that I couldn't do interesting sounding patches before. This is just different, and amazing to think that I am using just sine waves now and not reaching for the "ready made" waveforms.
I tried out programming additively just for kicks using a Casio fz1 back in the 90s, with 64 sines. Interesting, but massively labour intensive.
I can imagine!
Andy, some thoughts for your experiments. The formula for a saw wave: if the fundamental sine frequency F is volume level 1.0, then frequency 2F is 0.5, 3F 0.33 etc. If you scope that, the more sines you have, the more closely you approximate a sawtooth.

For square, omit any even F frequency multiplier.

For triangle, omit any even F frequency multiplier, and also divide the fundamental volume V by the frequency ratio squared. So F1= V F3= V/9, F5= V/25.
Thanks. That confirms what my own research has been telling me.
All harmonics should be in phase with the fundamental.
I think that the phase thing is something that I am struggling with. I mean, how on earth do I achieve that.

By "in phase" I am assuming that means, quite literally, that each sine wave must coincide exactly, and that their zero crossing points all match up where they should.

I thing that this image kind of confirms that:-

Image

But how do I ensure that that is happening with my various sine wave sources? Is there some way I should be synchronising them? I know that some modules have a "sync" option but I'm not sure that my Distings do.

I need to dig deeper into that.
Mordax data, or almost any DAW based EQ will show you what harmonics are doing very easily, just run a sawtooth in tuned at 50Hz... you can see the harmonics easily.
I'd love Mordax Data but I can't afford the outlay for that at the moment. So, yeah, I have to rely on my DAW.

I use Voxengo SPAN for the spectrum analysis and I have Melda Production's oscilloscope, which seem to work quite well.
Digital is absolutely the way to go for additive. Odessa looks very interesting. Wavetables can get you part way there, for example, E352/370 have some tables where harmonics fade up through the table.
All more money that haha :mrgreen:

Bottom line for me, at the moment, is I have up to six pure sine waves at my disposal and, potential phasing issues aside, I can have loads of fun messing around and seeing what I can come up with. I love doing drone stuff so this is something I am going to use in the future, for sure, and because I never do live stuff I can do loads of layering in my DAW to hopefully develop new and more interesting sounds.

cheers, and thanks for your input :)

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Re: Harmonic Series

Post by synkrotron » Thu May 21, 2020 4:31 am

Hi cornutt :)
cornutt wrote:
Wed May 20, 2020 9:27 pm
I've done some additive synthesis. IMO it's a synthesis method that is better done in software. You'd need a rather large system full of VCOs, LFOs, EG, VCAs and mixers to duplicate what you can do with a fairly basic additive plug-in like Minky Starshine (one of my most-used plug-ins). It is, however, practical to do a sort of hybrid method in software. E.g:

1. Mix a few sine waves, set to lower harmonics, and run them through a VCA with an envelope, and then mix that with the output of a conventional subtractive patch.

2. Do a simple mix of a few sine waves and then use them as the carrier in a ring modulator patch.

3. MIx several sine waves as, say, a fundamental with a 3rd, 6th, and 8th harmonic. (You'll probably have to use a frequency counter to do this accurately.) Then... pull out the patch cord for the fundamental, and mix the rest and give them a percussive envelope. You'll get bell-like sounds.

You can also try doing additive techniques with triangle waves. They have a little bit of harmonic content, and will add more "body" to additive patches with only a few oscillators, but not so much that the patch starts to dissolve into chaos the way it would if you were using, say, sawtooth waves.
Thanks for that, I'll be coming back to this in the near future and trying out some of those things :tu:

cheers

andy

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Re: Harmonic Series

Post by Keltie » Thu May 21, 2020 10:40 am

synkrotron wrote:
Thu May 21, 2020 4:29 am


I think that the phase thing is something that I am struggling with. I mean, how on earth do I achieve that.

By "in phase" I am assuming that means, quite literally, that each sine wave must coincide exactly, and that their zero crossing points all match up where they should.

I thing that this image kind of confirms that:-

Image

But how do I ensure that that is happening with my various sine wave sources? Is there some way I should be synchronising them? I know that some modules have a "sync" option but I'm not sure that my Distings do.

I need to dig deeper into that.
yep, thats right, all of the harmonics should start at zero degrees at the same instant. You're right that sync is the way to do it. You could rely on a multed note trigger to all of your sync ins ( assuming you have them.) A sneakier, and perhaps better way, is to take a Square out from your fundamental, and mult that to all of the syncs on the harmonics. Taking the example of a long note, and the first method, there is only one sync signal, and the tunings need to be dead on. Using the second technique, all syncs are refreshed at every cycle of the fundamental.

Although, of course, theres nothing to say you can't let sync drift, or experiment in lots of other ways. One example, I think referred to above, are the various formulations such as SQ at -1 oct + Sine, + harmonics, Reverse phase saw plus..... etc etc.

One last thought, Disting has wavetable mode, and can load these AFAIK, so theres some possibilities there to tide you over whilst you arrange to sell your kidneys for Odessa / Synth Tech :mrgreen:
synkrotron wrote:
Thu May 21, 2020 4:29 am

cheers, and thanks for your input :)
Yeah, no worries, have fun!

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Re: Harmonic Series

Post by oberdada » Thu May 21, 2020 12:04 pm

Yes, I'd think that for practical purposes sync as described would be fine and some drift should not matter much. However, restarting the waveform with sync will introduce a discontinuity so the sinus will have its own harmonic series which will be prominent if this occurs regularly and the step is somewhat large.

Additive synthesis is by no means limited to harmonic sounds. Weakly inharmonic sounds such as piano and other string instrument tones have slightly stretched spectra with higher partials being increasingly higher as compared to true harmonics. Also if you look up or analyse partial relations for metal bars (for example those of a vibraphone) or bells you might be able to approximate those sounds quite well with just three or four partials and the right envelopes. For better realism, more high partials should be present if the note is louder.

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Re: Harmonic Series

Post by synkrotron » Thu May 21, 2020 4:35 pm

Hi again :)
Keltie wrote:
Thu May 21, 2020 10:40 am
yep, thats right, all of the harmonics should start at zero degrees at the same instant. You're right that sync is the way to do it. You could rely on a multed note trigger to all of your sync ins ( assuming you have them.) A sneakier, and perhaps better way, is to take a Square out from your fundamental, and mult that to all of the syncs on the harmonics. Taking the example of a long note, and the first method, there is only one sync signal, and the tunings need to be dead on. Using the second technique, all syncs are refreshed at every cycle of the fundamental.
I am sure that the B7 algorithm of the Disting doesn't have a sync option. I'll have to ask os.

So I don't think that it is possible to get all those sine wave lined up :despair:
Although, of course, theres nothing to say you can't let sync drift, or experiment in lots of other ways. One example, I think referred to above, are the various formulations such as SQ at -1 oct + Sine, + harmonics, Reverse phase saw plus..... etc etc.
Yeah, I think that this is the route I'm going to take now, that is, experiment.

When I first decided to try additive stuff with my separate oscillators I was quite excited about it. But the reality is, it isn't truly additive, in terms of true harmonic series stuff.

In an experiment earlier I found that if the tuning wasn't bang on then that produced some strange results. So it's not just getting the phase right.

But that said, what I have learned is that going through that process of trying to emulate additive principles and the harmonic series "rules," if you like, and modulating the level of each element does give some very pleasing results. So that still has to be a positive, I think :)
One last thought, Disting has wavetable mode, and can load these AFAIK, so theres some possibilities there to tide you over whilst you arrange to sell your kidneys for Odessa / Synth Tech :mrgreen:
LOL! Yeah, well, wavetable synthesis is another area that I have only recently touched upon. Sounds like I've only just picked up "sound design" but I've been doing this for over nearly forty years. I have always stuff to what I know, which is (or was) subtractive synthesis.


cheers, and thanks again :)

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Re: Harmonic Series

Post by synkrotron » Thu May 21, 2020 4:39 pm

Hi :)
oberdada wrote:
Thu May 21, 2020 12:04 pm
Yes, I'd think that for practical purposes sync as described would be fine and some drift should not matter much. However, restarting the waveform with sync will introduce a discontinuity so the sinus will have its own harmonic series which will be prominent if this occurs regularly and the step is somewhat large.

Additive synthesis is by no means limited to harmonic sounds. Weakly inharmonic sounds such as piano and other string instrument tones have slightly stretched spectra with higher partials being increasingly higher as compared to true harmonics. Also if you look up or analyse partial relations for metal bars (for example those of a vibraphone) or bells you might be able to approximate those sounds quite well with just three or four partials and the right envelopes. For better realism, more high partials should be present if the note is louder.

Thank you very much for your input.

As you may be able to tell from my previous post, I am now realising that doing proper additive synthesis using the harmonic series as a basis isn't really practical. I can still get nice sounds but I can't, for instance, create a straight saw wave from adding together the sine waves that I have to hand.

You are mentioning stuff that is making me think that I should perhaps spend more time scrutinising my spectrum analyser :)

cheers

andy :)

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Re: Harmonic Series

Post by kvmet » Fri May 22, 2020 4:24 am

I have also been interested in harmonics/additive synthesis lately. I am actually (slowly, mind you) trying to DIY an additive synth as I learn more about it. I think doing it digitally is fairly straightforward since you can guarantee that everything remains in-phase (the hardest part actually being the sine calculations and not running out of compute cycles if it's running on a small chip).

There are some other neat things about it like transitioning between two different sets of gains for each harmonic. It would effectively act like a wavetable synth, but you just smoothly adjust the gains between the two different points.

Also if it's digital, adding frequency or phase modulation into the mix is easy. You just tweak the instantaneous frequency or phase angle, respectively, at the time you run each calculation.

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Re: Harmonic Series

Post by oberdada » Sat May 23, 2020 2:58 pm

kvmet wrote:
Fri May 22, 2020 4:24 am
I think doing it digitally is fairly straightforward since you can guarantee that everything remains in-phase (the hardest part actually being the sine calculations and not running out of compute cycles if it's running on a small chip).
In practice you would have a wavetable for the sinus and one fractional index to the wavetable per oscillator. It can be made very efficient, but there will be a limit on the number of partials you can deal with. If several partials can be mixed into one wavetable you have group additive synthesis. There are interesting tricks for crossfading between two sets of wavetables for timbral morphing, and even small detunings of individual partials can be handled.

As long as you only consider additive synthesis of harmonic or nearly harmonic sounds, there really is no difference except for details of implementation between additive and wavetable synthesis.

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Re: Harmonic Series

Post by Aaronautical001 » Sun May 24, 2020 2:25 am

This is an area I’m not just learning about as well. I’m fortunate to have Just Friends in my rig, which puts out the fundamental and 5 subsequent outputs based on that. One thing I was playing about with last night is using ring modulation to generate subsequent harmonics in the series.

Synkrotron : If you have a ring modulator, you might consider seeing if this approach can generate additional harmonics - although you do get 2 related harmonics from ring modulation, so may need some filters.

I was actually using this approach in a feedback patch with dark matter which seems to provide some pleasing results, but I need to investigate more to figure out what’s going on.

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Re: Harmonic Series

Post by synkrotron » Sun May 24, 2020 3:41 pm

kvmet wrote:
Fri May 22, 2020 4:24 am
I have also been interested in harmonics/additive synthesis lately. I am actually (slowly, mind you) trying to DIY an additive synth as I learn more about it. I think doing it digitally is fairly straightforward since you can guarantee that everything remains in-phase (the hardest part actually being the sine calculations and not running out of compute cycles if it's running on a small chip).

There are some other neat things about it like transitioning between two different sets of gains for each harmonic. It would effectively act like a wavetable synth, but you just smoothly adjust the gains between the two different points.

Also if it's digital, adding frequency or phase modulation into the mix is easy. You just tweak the instantaneous frequency or phase angle, respectively, at the time you run each calculation.
Thank you for your input :)
Aaronautical001 wrote:
Sun May 24, 2020 2:25 am
Synkrotron : If you have a ring modulator, you might consider seeing if this approach can generate additional harmonics - although you do get 2 related harmonics from ring modulation, so may need some filters.
Hi, yes, I do have a ring modulator, the one that came with my Doepfer system, so quite basic. And I am embarrassed to admit that I haven't used it for quite a while.

Thank you for mentioning it :)

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